## Abstract

We prove some local estimates on the trace of spectral projectors for random Schrödinger operators restricted to cubes ⊂ R^{d} . We also present a new proof of the spectral averaging result based on analytic perturbation theory. Together, these provide another proof of the Wegner estimate with an explicit form of the constant and an alternate proof of the Birman-Solomyak formula. We also use these results to prove the Lipschitz continuity of the local density of states function for a restricted family of random Schrödinger operators on cubes ⊂ R^{d}, for d 1. The result holds for low energies without a localization assumption but is not strong enough to extend to the infinite-volume limit.

Original language | English |
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Title of host publication | Schrödinger Operators, Spectral Analysis and Number Theory - In Memory of Erik Balslev |

Editors | Sergio Albeverio, Anindita Balslev, Ricardo Weder |

Pages | 117-132 |

Number of pages | 16 |

DOIs | |

State | Published - 2021 |

Event | Conference to celebrate Erik Balslev’s 75th birthday, 2010 - Aarhus, Denmark Duration: Oct 1 2010 → Oct 2 2010 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 348 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | Conference to celebrate Erik Balslev’s 75th birthday, 2010 |
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Country/Territory | Denmark |

City | Aarhus |

Period | 10/1/10 → 10/2/10 |

### Bibliographical note

Publisher Copyright:© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021.

## Keywords

- Density of states
- Random schrödinger operators
- Spectral averaging

## ASJC Scopus subject areas

- General Mathematics

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